标题： 一种用于具有不连续通量的LWR交通模型的半离散拉格朗日-欧拉格式 显示英文标题

标题： A Semidiscrete Lagrangian-Eulerian scheme for the LWR traffic model with discontinuous flux

摘要： 在本工作中，我们提出了一种半离散格式来逼近具有空间不连续通量的标量LWR交通模型的解，该模型由方程$u_t + (k(x)u(1-u))_x = 0$描述。这种方法基于E. Abreu、J. Francois、W. Lambert和J. Perez [J. Comp. Appl. Math. 406 (2022) 114011]为标量守恒律提出的拉格朗日-欧拉方法。我们推导了近似解的总变差增长速率的非均匀界。由于总变差只能在$x=0$处爆炸，我们可以通过使用Helly紧致性定理在$BV_{loc}(\mathbb{R}\setminus \lbrace 0 \rbrace)$中为我们的格式提供收敛性证明。 显示英文摘要

摘要： In this work, we present a semi-discrete scheme to approximate solutions to the scalar LWR traffic model with spatially discontinuous flux, described by the equation $u_t + (k(x)u(1-u))_x = 0$. This approach is based on the Lagrangian-Eulerian method proposed by E. Abreu, J. Francois, W. Lambert, and J. Perez [J. Comp. Appl. Math. 406 (2022) 114011] for scalar conservation laws. We derive a non-uniform bound on the growth rate of the total variation for approximate solutions. Since the total variation can explode only at $x=0$, we can provide a convergence proof for our scheme in $BV_{loc}(\mathbb{R}\setminus \lbrace 0 \rbrace)$ by using Helly's compactness theorem.